Both dramas give rise to the question of good and evil in humans and whether that is something out of our control or not. Bloody Monday have a genius hacker with the japanese special forces at its center, looking for his dad (and the mystery of his disappearance) while fighting against a group of terrorist wanting to "reset" the humanity. I remember you focuses on a genius consulting detective wanting to solve the forgotten mystery of his rather unfortunate past, while looking for his missing brother and along the way solving various crimes & clues that bring him closer to the core of the human psyche and the hazy gray zone of what is right and what is wrong. Both dramas are full of suspense as well as various plot twists.

One of the main leads in both dramas travel back in time by falling into water, but Go Princess Go puts an extra twist to the concept with it being a guy waking up in a girls body, which kinda adds another dimension to the ensuring love story. However, neither lead seems to be overly concerned to have traveled in time and neither tries to intentionally (yet) change any course of action in history (such as e.g. Faith) while being perceived as a bit weird/too freely spoken by the other characters. Moon Lovers is more visually stunning while Go Princess Go relies on some sassy comedy.

Both dramas incorporate modern elements, Moon Lovers seems to be big on modern themed music while Go Princess Go tries its hand on more visual and modernized outfits & settings.

Similar cinematography with pretty landscapes and sharp visuals. There is a sick/disabled romantic lead in both dramas, though with completely different back stories. Prepare for painful melo in both.

A girl living with three main guys, though under totally different premises; one is cross-dressing to cover for her twin brother in a upcoming boy band while the other one needs a place to stay and gets roped into this arrangement with the promise of college tuition.

All the guys have their own distinct, predetermined character, e.g. the rebel, the playboy, the artistic guy, the soothing/calm guy. And of course there's some kind of birth secret acting as a back drop to all of the drama that is to come. Also, not to forget the persistent ex-girlfriend/romantic interest.

I would say that you're beautiful has a more quirky sense of humor while cinderella is a bit superficial in regards of character depth, both filled with clichéd romance :)

Similar type of set up with the main couple coming to live together because of a certain misunderstanding/deceiving, the girl likes the guy first while he still has lingering feelings for his cunning first love until he gradually starts falling in love with the meddlesome main girl.

There's no angry mom in Gokusen but there is some organized crime involved but more like Han Gong Ju-style, there is a righteous teacher, a stupid vice principal and unruly students, but also some rather preachy dialogues/monologues. Regardless, both are a fun watch with darker themes (Angry Mom is upfront with it, if not a bit gory at times while Gokusen is more careful, mostly if you care to think hard and long enough since Gokusen's premise relies more on comedy) as the students mature and grow through their actions.

If you liked the quirky characters and the humor in one drama then the other might suit your taste :) I would say that both of these dramas have a similar feeling and ironical take on life, even if Ho Goo's Love is way more humorously darker. Also, all characters doesn't seem far too predictable and have their own drive, which is not always directly revealed for the viewer.